We consider the problem of finding a linear iteration that yields distributed averaging
consensus over a network, ie, that asymptotically computes the average of some initial …

The analysis and optimization of complex systems can be reduced to mathematical
problems collectively known as combinatorial optimization. Many such problems can be …

This software package is a MATLAB implementation of infeasible path-following algorithms
for solving standard semidefinite programs (SDP). Mehrotra-type predictor-corrector variants …

Optimization is one of the most important areas of modern applied mathematics, with
applications in fields from engineering and economics to finance, statistics, management …

Minimization with orthogonality constraints (eg, X^ ⊤ X= I) and/or spherical constraints (eg,
‖ x ‖ _2= 1) has wide applications in polynomial optimization, combinatorial optimization …

We examine the problem of approximating, in the Frobenius-norm sense, a positive,
semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality …

In this paper, we present a nonlinear programming algorithm for solving semidefinite
programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of …

We consider a symmetric random walk on a connected graph, where each edge is labeled
with the probability of transition between the two adjacent vertices. The associated Markov …

Convex relaxations have emerged as a promising approach for verifying properties of neural
networks, but widely used using Linear Programming (LP) relaxations only provide …

In this paper we improve upon the running time for finding a point in a convex set given a
separation oracle. In particular, given a separation oracle for a convex set K⊂ R n that is …